Generally cheaper - $100 for a new 8x10 silnylon, $200 for cuben
Save a lot of weight - silnylon 8x10 will weigh ~15oz, cuben ~7oz. Can easily put together a sub-1-lb shelter/bug solution for $300ish, which is about what you pay for a new 2lb tent.
Versatility of pitches - pitch it high for ventilation so you avoid condensation, low to the ground for wind blown rain, pitch one side to the ground and leave the other open, etc.
Depending on size of the tarp, much more space to move around during a storm. Also more room for your gear.
Trivial to pack up in the rain - don't have to worry about keeping the interior of a tent dry. Just pack up all your other stuff and then take down the tarp last.
Can cook underneath it more comfortably and safely than cooking in a tent vestibule.
Easier to find camp spots - you don't have a big bathtub floor to worry about, so you don't need as much completely clear ground which can be hard to find in dense forest. Can pitch it over small shrubs, etc.
More versatile setup especially on the AT if you are a shelter person - use the tarp alone if no bugs, cowboy or use bivy if no rain, use the bivy inside a shelter for bug protection, use tarp to block wind/rain coming into shelter.
A tarp with enough pullouts, stakes, guylines will also be more storm worthy than many ultralight tents due to the fact that you can get the fabric very taut if you pitch it right.
Easier to pee at night...
Nice views, easier to identify night time noises